Question: Solve for $x$ and $y$ using elimination. ${-4x-y = -9}$ ${-5x+y = -9}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $-9x = -18$ $\dfrac{-9x}{{-9}} = \dfrac{-18}{{-9}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-4x-y = -9}\thinspace$ to find $y$ ${-4}{(2)}{ - y = -9}$ $-8-y = -9$ $-8{+8} - y = -9{+8}$ $-y = -1$ $\dfrac{-y}{{-1}} = \dfrac{-1}{{-1}}$ ${y = 1}$ You can also plug ${x = 2}$ into $\thinspace {-5x+y = -9}\thinspace$ and get the same answer for $y$ : ${-5}{(2)}{ + y = -9}$ ${y = 1}$